Elsevier

Advances in Engineering Software

Volume 38, Issues 11–12, November–December 2007, Pages 802-809
Advances in Engineering Software

Simulation of cerebrospinal fluid transport

https://doi.org/10.1016/j.advengsoft.2006.08.032Get rights and content

Abstract

The pulsatile nature of the CSF movement is a result of the cardiac-related pulsations in blood volume in cranial region. According to Monro–Kellie Doctrine, the net inflow of arterial blood during systole is compensated by an equal outflow of venous blood and by caudal displacement of the CSF. Knowledge of the distribution of physical properties (compliance, resistance) along the craniospinal system is crucial for understanding of the CSF hydrodynamics. The synthesis of both invasively and non-invasively obtained data is needed. The aim of our project was to develop a lumped-parameter compartment model of the craniospinal system and, in relation to the cardiac-related blood-volume pulsations, to describe its basic hydrodynamic properties. The model consists of six compartments representing major parts of the craniospinal system. Each compartment has its own set of physical properties which describe its behavior. The pressure transmission from head arteries to the brain compartment serves as a source of pulsations. The simulation tightly mimics pressure waves of the CSF and thus the flow characteristics and magnitudes. The fitted compliance of the spinal compartment in our model was two orders higher (9 × 10−10 m3/Pa) then the cranial compartment (5.2 × 10−12 m3/Pa): only in this adjustment pulsations were present. It makes 99.5% of compliance related to the spinal canal and 0.5% to the intracranial structures. Our fitting showed that this model might be used in medical education as well as in medical practice.

Introduction

The knowledge of hydrodynamic processes in the CSF transportation system has been increasingly emphasized in the past decades. Its importance is even more accented by the necessity to treat patients suffering from illnesses with relationship to the CSF hydrodynamics pathology (hydrocephalus, syringomyelia, Chiari malformations, craniotrauma, etc.) [1], [2], [3], [4]. A key function of the CSF is the protection of CNS (it lowers the effects of gravity on CNS and softens the force effects of body vibrations). The CSF also offers an alternative path for the distribution of a variety of mediators, neuropeptides, hormones and ions to the target cells in brain and spinal cord. The CSF plays an important role in displacement of metabolic products of nervous tissue as well as in its temperature balance by conduction of an excessive heat [5].

According to the traditional view, the CSF flows slowly and constantly from its major source (choroid plexus) to its main resorption point in arachnoidal granulations. The changes in the production are considered to balance the changes in absorption under normal physiological conditions. However, data from MRI flowmetry showed that slow bulk CSF flow appears to exist only inside the ventricular system (along with the pulsatile flow), but there is no evidence of this kind of flow in intracranial or spinal subarachnoidal spaces where the flow appears to be pulsatile [6], [7]. The pulsatile nature of the CSF movement is a result of the cardiac-related pulsations in blood volume in cranial region [8], [9], [10]. According to Monro–Kellie Doctrine, the net inflow of arterial blood during systole is compensated by an equal outflow of venous blood (constant) and by caudal displacement of the CSF (pulsatile, as the total volume of intracranial contents must remain constant) [6], [8], [9].

Knowledge of distribution of physical properties (compliance, resistance) along the system is crucial for understanding of the CSF hydrodynamics. In present, however, major theories concerning compliance and resistance rely mainly on data obtained from direct CSF pressure measurements. Direct pressure measurement is invasive and significantly modifies physiological CSF dynamics. Therefore, its interpretation should be cautious. Moreover, results from non-invasive techniques, such as MRI or ultrasound, describe precisely only the flow of the CSF and movement of the CNS structures. Thus synthesis of both direct and indirect obtained data is needed.

Lumped-parameter models represent a suitable method for examining flow dynamics involving complicated human physiology. In this approach, the biological system is divided into a number of interconnected compartments. Dynamics in each compartment is specified by lumped, time-dependent functions giving compartmental pressures, while incremental changes in flows and compartmental volumes are obtained by associating resistance and compliance parameters with adjacent compartments [11], [12].

The aim of our project was to develop a lumped-parameter compartment model of the craniospinal system and, in relation to the cardiac-related blood-volume pulsations, to describe its basic hydrodynamic properties. The model consists of six compartments representing major parts of the craniospinal system. Each compartment has its own set of physical properties which describe its behavior. The pressure transmission from head arteries to brain compartment serves as a source of pulsations. Basic physical laws (conservation of mass and conservation of momentum) were used in accordance with the Monro–Kellie Doctrine.

Section snippets

Methods

The model extends an existing numerical lumped-parameter compartment model of the hemodynamics of the whole human cardiovascular system (CVS) which was developed at the Institute of Thermomechanics of Academy of Sciences of the Czech Republic [12]. Briefly, the whole circulatory system is modelled by four compartments representing the pulsating heart and by 10 vascular segments of the pulmonary and systemic circuits (including intracranial circulation) connected with the heart in series (for

Results

The result of this project is the lumped-parameter model that describes pulsatile flow of CSF in the whole craniospinal system. The craniospinal system consists of six compartments. Each compartment is defined by its compliance, pressure, residual and current volume and linear constant of the CSF formation/resorption. The forcing of this system is provided by the transmission of volume/pressure pulsations in cerebral arteries to compartment L1. The transmission itself was modulated by a linear

Discussion

Many authors aimed their efforts to describe hydrodynamic processes in the cerebrospinal system by experimental measurement or by numerical simulation because of its high clinical impact. In present, direct non-invasive MRI and ultrasound measurements of the CSF flow are common. However, these methods by themselves do not describe physical properties of the system and, moreover, the measurement is limited to small regions of interest. On the other side one can use direct measurement of the

Conclusions

Our model of the cerebrospinal fluid transportation simulates all major properties of this system. Fitting to physiological conditions showed that system must be finely tuned on the heart rate to exhibit cardiac-related pulsation by setting exact time constant defined by RC. Higher compliance of the spinal part of the system is needed to mimic gradual reduction in both pressure and flow magnitudes. The model is usable for synthesis of data coming from different measurement methods. This

Acknowledgements

This project was supported by grants No. 106/03/0958 of the Czech Science Foundation and by grants Nos. 112/2005 and 114/2005 of the Grant Agency of the Charles University in Prague. Excellent assistance of V. Štembera and S. Převorovská is acknowledged.

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